PARIS, May 29 (Reuters) - The European Union needs to set simple rules on bank capital to complete its banking union under a sole EU-wide sector supervisor, ECB Governing Board member Francois Villeroy de Galhau said on Monday.

Speaking in Paris in his role as head of the ACPR French financial sector regulator, Villeroy said the EU also needed better coordination between the single supervisor at the European Central Bank, the European Commission and national regulators.

"Two and a half years after banking union, there has been clear progress, but its construction is not yet finished. We need to finish the resolution pillar with completed and more simple rules," Villeroy told journalists.

Villeroy also called for a rapid solution to bank troubles in Italy and Portugal, saying it was "not normal" that local problems weighed on the image of the overall European banking sector.

He also reiterated a call for the clearing of large euro transactions to be done in countries covered by the ECB's supervision.

"After Brexit, we don't see how this could be in London," he added. (Reporting by Leigh Thomas; Editing by Sudip Kar-Gupta)